1. Field of the Invention
This invention is related in general to the field of dive computers. In particular, the invention consists of a method for calculating the formation of free gas in a human body due to a change in altitude, depth, or pressure.
2. Description of the Prior Art
An undersea diver needs to breathe air or some other gas mixture at a pressure that closely matches the pressure of the surrounding water. The pressure exerted on the diver increases dramatically as he increases his depth under the surface of the water. As a result, the concentrations or ‘tensions’ of dissolved inert gases in his body tissue can rise well beyond the levels than are common above the water surface.
Of special consequence is the inert gas nitrogen, which comprises 79% of the volume of air under normal atmospheric conditions. During a dive, excess nitrogen becomes dissolved in the body's tissues. The amount of nitrogen which is absorbed by the body's tissues is a function of the depth of the dive and the amount of time at this depth.
While dissolved, the nitrogen undergoes no reactions with the tissue. However, as the diver rises to the surface, the nitrogen leaves the body's tissues and travels through the diver's bloodstream, where it may be released as free gas. This released free gas may result in decompression sickness, which can result in pain, disability, or death of the diver. In order to reduce the likelihood of decompression sickness, a diver may need to slowly rise to the surface or stop at intervals along the way.
Decompression Sickness
Decompression sickness made its first appearance in the mid-nineteenth century among men who worked in submerged caissons to set the footings of bridges like the Brooklyn Bridge. At the time, the affliction was called caisson workers' disease. The symptoms were acute joint pain following emergence from the high pressure atmosphere in the caissons. Victims would often bend over in pain, so the affliction became commonly known as “the bends”. The bends were clearly caused by the fall in air pressure or “decompression” as the victims passed from submerged caissons to the surface, but the physiology remained otherwise obscure, an obscurity that persists to some degree today.
Haldane Models
The first systematic studies of caisson disease or decompression sickness were conducted at the start of the last century, stimulated by the appearance of the same symptoms among deep sea divers, who were subject to the same type of decompression as caisson workers. That early research culminated in a brilliant paper by Haldane and co-workers, who argued that “compressed air sickness” is caused by absorption of nitrogen in tissue during the compressive phase of a dive, followed by its release in gaseous form during decompression (Boycott, Damant, and Haldane 1908). Haldane and his group conducted extensive pressure chamber tests on goats and compared the results with divers' experience.
The Haldane group also developed a mathematical model of decompression sickness based on the idea that tissue absorbs nitrogen at a rate proportional to the difference between the partial pressure of nitrogen in the lungs and the “tension” of nitrogen dissolved in tissue and blood. They discovered that absorption at a single rate would not explain their data, and they conceived the idea of multiple “tissue compartments” with different rates of nitrogen absorption. Multiple tissue compartments with different absorption rates have come to be known as the “Haldane model”. Almost 100 years after its conception, the Haldane model remains the basis for today's dive computers.
The Haldane group posited five tissue compartments with absorption rates equivalent to half times of 5, 10, 20, 40, and 75 minutes. They assumed that a diver would suffer decompression sickness if the nitrogen tension in any one of the compartments reached a specific load common to all of the compartments. The nitrogen load was measured not in terms of concentration (ml/ml) or tension (mm Hg) but in terms of the depth where the nitrogen concentration would be in equilibrium with the air being breathed. Thus the critical nitrogen load was expressed in terms of feet of sea water (fsw).
Subsequent workers increased the number of hypothetical tissue compartments and assigned to them different critical nitrogen loads. Workman (1965) proposed six tissue compartments with half times of 5, 10, 20, 40, 80, and 120 min and assigned to them critical loads ranging from 100 down to 20 fsw. Workman's variant of the Haldane model became the basis for the US Navy dive tables and for the first generation of dive computers (Lewis and Shreeves 1993). More recent dive computers have increased the number of hypothetical compartments to twelve, and Lewis and Shreeves even invoke the ultimate dive computer HAL with 1530 tissue compartments and 3060 half times and loads! However, Hills (1977) has observed with amusement that the larger Haldane models have more parameters than data available to be fitted by them.
The largest relevant data set was published by Hamilton, Rogers, Powell, and Vann (1994) under the title “The DSAT Recreational Dive Planner”. The data are the results of 2943 dives, some in water, and some simulated in a pressure chamber at the Institute of Applied Physiology and Medicine in Seattle. To determine dive profiles with low risks of decompression sickness, they fitted the parameters of a Haldane model to an earlier data set of Spencer (1976). Only 301 or 10% of those dives produced measurable bubbles, and only one caused decompression sickness, an incidence rate of 0.03%. The Haldane parameters established by Hamilton et al. are the basis for many of the dive computers in use today.
Other Models
Despite their widespread use, the Haldane models invite some reservations. One is the notion of “tissue compartments”, which never have been correlated with physiological structures. Another is “perfusion”, the means by which gas is supposed to travel from the lungs into tissue. Perfusion describes the Haldane models but not an actual gas transport mechanism.
Among the first to try to improve upon those concepts was Hempleman (1952), who suggested that gas absorption could be modeled as a process of diffusion from blood vessels into homogeneous tissue. He first modeled the tissue as a one-dimensional slab bounded on one side by blood and unbounded on the other. An immediate result of that very simple model is that the mass of nitrogen absorbed during a dive is proportional to the partial pressure P of nitrogen above its value at sea level times the square root of the duration T of the dive. Hempleman assumed that the product “P-root-T” must remain below some allowable value for safe return to the surface. He determined the allowable limit by comparison with Workman's data, with the result that P-root-T is around 500 fsw−√{square root over (min)}. In 1968, Hempleman's simple model became the basis for the Royal Navy Dive Tables.
However, one-dimensional diffusion into an infinite slab could not allow for saturation, since the slab would absorb nitrogen indefinitely. To allow for saturation, Hempleman analyzed diffusion into a finite slab and obtained an infinite series of terms bearing a resemblance to Haldane “tissue compartments”. The finite slab model did not improve agreement with Workman's data and may never been used for dive computers.
The most obvious limitation of both the Haldane and Hempleman models is that they make no attempt to predict the formation of free nitrogen gas, the presumptive cause of decompression illness. The emphasis instead is on nitrogen storage in form of molecules dissolved in tissue. This lack to attention to a model for free gas formation is particularly odd for the Haldane group, who observed nitrogen gas bubbles in the eyes of severely afflicted goats.
Hills (1966, 1977) may have made the first serious effort to understand gas formation as a cause of decompression sickness. He proposed that gas volumes form in tissue wherever net gas tension exceeds the local ambient pressure, and he drew attention to the fact that any such gas cells would contain the so-called metabolic gases, oxygen, carbon dioxide, water vapor, and nitrogen. Many of Hills's physiological insights were brilliant, but they were not pulled together into a mathematical model of decompression sickness. Additionally, his qualitative proposal for gas formation would have resulted in calculations indicating far too much gas being formed in tissue, e.g., several liters for dives to 100 ft. Also, his proposed ascent strategies are clearly at odds with the experience of divers (Gernhardt 1991).
A nitrogen gas concept finally made its way into Haldane models as RGBM, the Reduced Gradient Bubble Model (Wienke 1990, 2003). The basic idea is that nitrogen filled microbubbles pervade body tissue at all times, even without dives and ascents. Without a special sustaining mechanism, gas in the hypothetical bubbles would diffuse into surrounding tissue in minutes, and the bubbles would close. Wienke assumes that “flexible seed skins” keep the bubbles open while a diver is on the surface or descending under water. During ascent, gas diffuses into the microbubbles, and they enlarge in accord with Boyle's law for expansion at constant temperature. The presumed presence of the bubbles reduces the allowable nitrogen loads of the Haldanian tissue compartments. The Gradient in the Reduced Gradient Bubble Model is proportional to the difference between the allowable Haldane tissue compartment loads and the partial pressure of nitrogen at sea level.
However, the Reduced Gradient Bubble Model has to assume the perpetual existence of gas bubbles held open by “flexible seed skins”. The concept of perpetual gas bubbles, moreover, conflicts with the common observation that bubbles in supersaturated liquids form on boundaries, not in the interiors of liquids (Knapp, Daily, and Hammitt 1970). The Reduced Gradient Bubble Model does not supercede the Haldane models, but rather changes the allowable nitrogen loads in response to specific dive scenarios, e.g., reversed dive profiles. Finally, the Reduced Gradient Bubble Model is not a real-time algorithm. RGBM computations are traditionally performed on a mainframe computer and incorporated into dive computers as modified Haldane allowable nitrogen loads.
Based on these models, the sport diving industry has developed dive computers to guide divers with regard to allowable times at depth and ascent procedures to avoid decompression sickness. Traditional dive computers measure time and water pressure, and perform computations to indicate the time a diver may remain at a particular depth and the recommended ascent procedures to minimize the possibility of decompression sickness.
However, these algorithms are not based on physiology and make no prediction with regard to the formation of free nitrogen. As a consequence, the algorithms are of uncertain validity when used outside of the dive data upon which they are based. Accordingly, it is desirable to have a dive computer that utilizes an algorithm to calculate the potential formation of free nitrogen when utilized in conditions outside of those covered by existing dive tables.
Because these dive computers do not incorporate physiological parameters as inputs, the algorithms cannot be tuned with any certainty to the needs of individual divers. Also, because existing algorithms are not based on physiology, they cannot be upgraded with modern research in physiology. Accordingly, it is desirable to have a method of calculating the potential formation of free nitrogen in the human body that can take into account physiological parameters of the user.